Improving the earthquake performance of bridges using...
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Improving the earthquake performance of bridges using seismic isolation
Ian Buckle Professor, University of Nevada Reno
TRB Webinar February 10, 2016
Sponsored by TRB Committee AFF50: Seismic Design and Performance of Bridges
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Acknowledgements
• Many colleagues in: – Academia – DOT practitioners – Industry
• AASHTO SCOBS Committees T-2 (Bearings) and T-3 (Seismic Design)
• NCHRP 20-7 (262) Review and Update of the AASHTO
Guide Specifications for Seismic Isolation Design
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Outline
• Conventional vs seismic isolation design • History • Basic requirements (principles) • Examples (applications) • Limitations • Design of a bridge isolation system • Additional sources of information • Design examples • Q&A
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Outline
• Conventional vs seismic isolation design • History • Basic requirements (principles) • Examples (applications) • Limitations • Design of a bridge isolation system • Additional sources of information • Design examples • Q&A
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Conventional seismic design
• Fundamental requirement of seismic design: Capacity
> 1.0 Demand
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Demand
• But demand is excessive
Fsmax ~ 1.1W
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Demand
• Because demand is excessive it is often impractical to provided sufficient capacity to keep structure elastic
• Hence damage is accepted in form of plastic deformation and concrete spalling in ‘hinge zones’
capacity seismic design
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Conventional seismic design
• Since yield is permitted: Deformation Capacity
> 1.0 Deformation Demand
INCREASE CAPACITY
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Conventional seismic design
Deconstruction of Christchurch, 2011-12
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Conventional seismic design
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Alternative approach
Deformation Capacity
> 1.0 Deformation Demand
REDUCE
DEMAND
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Alternative approach
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Alternative approach
• Easiest way to reduce demand is to increase flexibility
and lengthen period, T
Fsmax ≈ 0.25W
Fsmax ≈ 1.1W
T = 0.5 sec T=1.5 sec
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Alternative approach
• This approach is essence of seismic isolation
– add flexibility to lengthen period to give a better ‘ride’
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Seismic isolation
• By lengthening period, substantial reductions in forces (e.g. base shear) are possible and often feasible to keep structure elastic during design earthquake (i.e. no yield)
• Significant reductions in repair costs • Continuing functionality is achievable • Applicable to new and existing structures • Applicable to buildings, bridges, industrial
plant…
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But…
• Increasing the period increases displacement
Dmax≈4.9 in
Dmax≈2.7 in
T=0.5 sec T=1.5 sec
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Force-displacement tradeoff
Period shift Spectral acceleration,
Period, T
Increased damping
Spectral displacement,
Period, T
Increased damping
T2 T1
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Force-displacement tradeoff
• Tradeoff between force and displacement is one of the challenging aspects of base isolation
• Additional damping is usually added to limit the increase in displacements
• Note that these ‘larger’ displacements occur mainly in isolator themselves and not in the structure (i.e. columns). Even though the system displacements may be ‘large’, column drift is small
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Outline
• Conventional vs seismic isolation design • History • Basic requirements (principles) • Examples (applications) • Limitations • Design of a bridge isolation system • Additional sources of information • Design examples • Q&A
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History – The Distant Past
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History – So. Rangitikei River Bridge, 1979
World’s First Base-Isolated Bridge
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History – William Clayton Building, 1981
World’s First Base-Isolated Building
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History - Today
• Today seismic isolation is but one member of a growing family of earthquake protective systems that includes: – Mechanical energy dissipators – Tuned mass dampers – Active mass dampers – Adaptive control systems – Semi-active isolation
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History - Today
EARTHQUAKE PROTECTION SYSTEMS
PASSIVE PROTECTIVE
SYSTEMS
HYBRID PROTECTIVE
SYSTEMS
ACTIVE PROTECTIVE
SYSTEMS
Tuned mass damper
Semi-active isolation
Active isolation
Adaptive control
Active braces
Active mass damper
Energy dissipation
Seismic isolation
Semi-active mass damper
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Outline
• Conventional vs seismic isolation design • History • Basic requirements (principles) • Examples (applications) • Limitations • Design of a bridge isolation system • Additional sources of information • Design examples • Q&A
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Basic requirements of isolation system
1) Flexible mount to lengthen period of the structural system
2) Damper (energy dissipator) to limit the displacement in the flexible mount
3) Restraint for service loads (wind, braking…) 4) Restoring device to re-centre system
following an earthquake
Above requirement- stiff for service loads, flexible for earthquake loads - means that all practical isolation systems are nonlinear.
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Basic requirements
Qd = characteristic strength
Fy = yield strength
Fmax= maximum isolator force
Kd = post-elastic stiffness
Ku = loading and unloading stiffness
Keff = effective stiffness
∆max (= umax)
= maximum isolator displacement
EDC = area of hysteretic loop
= energy dissipated per cycle.
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Basic properties
• Two most important properties are: – Qd: characteristic strength, pseudo yield – Kd: second slope, isolator stiffness after ‘yield’ – Qd and Kd determine effective stiffness (Keff) and
energy dissipated per cycle (EDC) for given displacement, ∆max
– Keff determines effective period Teff and – EDC determines equivalent viscous damping ratio, heff
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Basic requirements of isolation system
1) Flexible mount to lengthen period of combined structure-isolator system
2) Damper (energy dissipator) to control displacement in flexible mount
3) Restraint for service loads (wind, braking…) 4) Restoring device to re-centre system
following earthquake
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Basic requirements Requirement Examples Flexible mount Elastomeric bearing (natural or synthetic
rubber) Flat or curved sliding surface PTFE and stainless steel)
Damper Plastic deformation (steel, lead…) Friction Viscosity of fluid High damping rubber compound
Restraint Mechanical fuse Elastic stiffness of a yielding dissipator Friction (pre-slip)
Restoring device Elastomeric or metal spring Concave sliding surface
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Basic hardware Isolator Type Available devices Elastomeric systems Lead-rubber bearing (LRB)
-standard natural rubber bearing with lead core High damping rubber bearing (HDR) -modified natural rubber bearing with high damping rubber compound
Sliding Systems Concave friction bearing (CFB) -concave slider using PTFE and stainless steel Flat plate friction bearing (FPB) -flat plate slider using PTFE and stainless steel, and elastomeric springs
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Basic hardware
Left: Lead rubber bearing (LRB)
Right: Concave friction bearing (CFB)
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Basic hardware
Flat plate friction bearing (FPB)
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Outline
• Conventional vs seismic isolation design • History • Basic requirements (principles) • Examples (applications) • Limitations • Design of a bridge isolation system • Additional sources of information • Design examples • Q&A
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Applications: US 101 Sierra Point, CA
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Applications: I-680 Benicia-Martinez, CA
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Applications: JFK Airport Light Rail, NY
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Applications: Bolu Viaduct, Turkey
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Applications in U.S., Canada, Mexico
State Number of isolated bridges
Percent of total number of isolated bridges in
North America California 28 13% New Jersey 23 11% New York 22 11% Massachusetts 20 10% New Hampshire 14 7% Illinois 14 7% Total 121
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Applications in U.S., Canada, Mexico
Isolator Type
Applications (Percent of total
number of isolated bridges
in North America)
Lead-rubber bearing 75%
Flat plate friction bearing 20%
Other: Concave friction bearing, High damping rubber bearing, Natural rubber bearing
5%
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Outline
• Conventional vs seismic isolation design • History • Basic requirements (principles) • Examples (applications) • Limitations • Design of a bridge isolation system • Additional sources of information • Design examples • Q&A
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Limitations
• Successful application of isolation is dependent on the shape of the acceleration response spectrum
• Sites not suitable for isolation include those where the spectrum does not decay rapidly with increasing period, such as a soft soil site
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Limitations
Soft soil spectrumRock
spectrum
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Limitations
• Other sites where isolation is questionable include near-field sites where long period, high-velocity pulses may be encountered
• Bridges where isolation is questionable include those: – with tall piers that have long ‘fixed-base’ periods – in high seismic zones on soft sites where
superstructure displacements are large and movement joints expensive
• Exceptions exist…
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Conversely…
• Bridges most suitable for isolation include those – with relatively short ‘fixed-base’ periods (< 1.5 s) – on competent soils, and – not in near-field.
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Outline
• Conventional vs seismic isolation design • History • Basic requirements (principles) • Examples (applications) • Limitations • Design of a bridge isolation system • Additional sources of information • Design examples • Q&A
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Design of a bridge Isolation system
Three step process: 1. Select required performance criteria 2. Determine properties of the isolation system to
achieve required performance (e.g. Qd and Kd) using one or more methods of analysis
3. Select isolator type and design hardware to achieve required system properties (i.e. Qd and Kd values) using a rational design procedure
V
D
Kd Qd
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Performance criteria
• Usually set by owner • Examples include:
o Not-to-exceed total base shear for Design Earthquake (1,000 yr return period)
o Elastic columns during Design Earthquake (1,000 yr) o Not-to-exceed longitudinal displacement in
superstructure during Design Earthquake o Essentially elastic behavior for the Maximum
Considered Earthquake (MCE, 2,500 yr) o Reparable damage in MCE, but not collapse
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Analysis methods for isolated bridges
Bridges with nonlinear isolators may be analyzed using linear methods provided equivalent properties are used, such as • effective stiffness, and • equivalent viscous damping, based on the hysteretic energy dissipated by the isolators.
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Analysis methods for isolated bridges
• Uniform Load Method • Single Mode Spectral Method • Multimode Spectral Method • Time History Method
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Analysis methods
• Uniform Load Simplified Method • Single Mode Spectral Method • Multimode Spectral Method • Time History Method
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Assumptions in Simplified Method
1. Superstructure acts a rigid-diaphragm compared to flexibility of isolators
2. Single displacement describes motion of superstructure, i.e. single degree-of-freedom system
3. Nonlinear properties of isolators may be represented by bilinear loops
4. Bilinear stiffness can be represented by Kisol, effective stiffness. Note Kisol is dependent on displacement, D
Kisol
V
D
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Assumptions in Simplified Method
5. Hysteretic energy dissipation may be represented by viscous damping, i.e., work done during plastic deformation can be represented by work done moving viscous fluid through an orifice. Equivalent viscous damping ratio given by
6. Acceleration spectrum is inversely proportional to period (i.e. SA = a / T)
)1(2
isol
y
m
d
DD
FQh −=
π
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AASHTO Design Response Spectra AASHTO Spectra (SA) are for 5% damping on a rock site (Site Class B)
For sites other than rock, the spectra are modified by Site Factors, Fa and Fv
For damping other than 5%, the spectra are modified by a Damping Factor, BL
TBS
TBSFAS
L
D
L
vA
11 ==≡
L
D
L
vD B
TSB
TSFgDS 112
79.94
=
=≡
π
Period, T
SA (A) Spectral Acceleration (g)
SD1
1.0s
5 % damping
h % damping
SD1 / BL
Period, T
SD (D) Spectral Displacement
≈10SD1
1.0s
5 % damping
h % damping ≈10SD1 / BL
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Assumptions in Simplified Method
7. Acceleration spectra for 5% viscous damping may be scaled for actual damping (h) by dividing by a damping coefficient, BL
3.0
05.0
=
hBL
BL is used in long-period range of spectrum. Another factor (BS) is used in short-period range. Isolated bridges usually fall in long-period range.
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Simplified Method
Basic steps: 1. Assume value for Disol
2. Calculate effective stiffness, Kisol
3. Calculate max. force, Fm
4. Calculate effective period, Teff
disol
disol K
DQK += isolisolm DKF =
isoleff gK
WT π2=
Kisol
V
D
Disol
Fm Qd Kd
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Simplified Method continued
5. Calculate viscous damping ratio, h
6. Calculate damping coefficient, BL
7. Calculate Disol 8. Compare with value for
Disol in Step (1). Repeat until convergence.
)1(2
isol
y
m
d
DD
FQh −=
π3.0)
05.0( hBL =
effL
visol T
BSFgD 1
24π=
)(79.9 1 inchesTB
SFD effL
visol =
Kisol
V
D
Disol
Fm Qd Kd
Dy
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Example 1: Simplified Method
The superstructure of a 2-span bridge weighs 533 K. It is located on a rock site where SD1 = 0.55. The bridge is seismically isolated with 12 isolation bearings at the piers and abutments.
Isolation
system
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Example 1(a)
(a) If Qd = 0.075W and Kd = 13.0 K/in (summed over
all the isolators), calculate the maximum displacement of the superstructure and the total base shear. Neglect pier flexibility.
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Example 1(a) Solution Solution: 1. Initialize 1.1 Qd =0.075 W = 0.075 (533) = 40 K 1.2 Need initial value Disol Take Teff = 1.5 sec, 5% damping (BL=1.0) and calculate D = 9.79 SD1 Teff / BL = 9.79 (0.55) 1.5 = 8.08 in 2. Iterate 2.1 Set Disol = D and proceed with Steps 1-7
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Example 1(a) Solution contd.
Step Trial 1 Trial 2 Trial n
0. Characteristic strength, Qd 40.0 0. Post-elastic stiffness, Kd 13.0 1. Isolator Displacement, Disol
2. Effective stiffness, Kisol
3. Max. isolator force, Fm
4. Effective period, Teff
5. Viscous damping ratio, h% 6. Damping coefficient, BL
7. Isolator displacement, Disol
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Example 1(a) Solution contd.
Step Trial 1 Trial 2 Trial n
0. Characteristic strength, Qd 40.0 0. Post-elastic stiffness, Kd 13.0 1. Isolator Displacement, Disol 8.08
2. Effective stiffness, Kisol
3. Max. isolator force, Fm
4. Effective period, Teff
5. Viscous damping ratio, h% 6. Damping coefficient, BL
7. Isolator displacement, Disol
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Example 1(a) Solution contd.
Step Trial 1 Trial 2 Trial n
0. Characteristic strength, Qd 40.0 0. Post-elastic stiffness, Kd 13.0 1. Isolator Displacement, Disol 8.08
2. Effective stiffness, Kisol 17.95 3. Max. isolator force, Fm
4. Effective period, Teff
5. Viscous damping ratio, h% 6. Damping coefficient, BL
7. Isolator displacement, Disol
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Example 1(a) Solution contd.
Step Trial 1 Trial 2 Trial n
0. Characteristic strength, Qd 40.0 0. Post-elastic stiffness, Kd 13.0 1. Isolator Displacement, Disol 8.08
2. Effective stiffness, Kisol 17.95 3. Max. isolator force, Fm 144.9 4. Effective period, Teff
5. Viscous damping ratio, h% 6. Damping coefficient, BL
7. Isolator displacement, Disol
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Example 1(a) Solution contd.
Step Trial 1 Trial 2 Trial n
0. Characteristic strength, Qd 40.0 0. Post-elastic stiffness, Kd 13.0 1. Isolator Displacement, Disol 8.08
2. Effective stiffness, Kisol 17.95 3. Max. isolator force, Fm 144.9 4. Effective period, Teff 1.46 5. Viscous damping ratio, h% 6. Damping coefficient, BL
7. Isolator displacement, Disol
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Example 1(a) Solution contd.
Step Trial 1 Trial 2 Trial n
0. Characteristic strength, Qd 40.0 0. Post-elastic stiffness, Kd 13.0 1. Isolator Displacement, Disol 8.08
2. Effective stiffness, Kisol 17.95 3. Max. isolator force, Fm 144.9 4. Effective period, Teff 1.46 5. Viscous damping ratio, h% 17.6 6. Damping coefficient, BL
7. Isolator displacement, Disol
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Example 1(a) Solution contd.
Step Trial 1 Trial 2 Trial n
0. Characteristic strength, Qd 40.0 0. Post-elastic stiffness, Kd 13.0 1. Isolator Displacement, Disol 8.08
2. Effective stiffness, Kisol 17.95 3. Max. isolator force, Fm 144.9 4. Effective period, Teff 1.46 5. Viscous damping ratio, h% 17.6 6. Damping coefficient, BL 1.46 7. Isolator displacement, Disol
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Example 1(a) Solution contd.
Step Trial 1 Trial 2 Trial n
0. Characteristic strength, Qd 40.0 0. Post-elastic stiffness, Kd 13.0 1. Isolator Displacement, Disol 8.08
2. Effective stiffness, Kisol 17.95 3. Max. isolator force, Fm 144.9 4. Effective period, Teff 1.46 5. Viscous damping ratio, h% 17.6 6. Damping coefficient, BL 1.46 7. Isolator displacement, Disol 6.43
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Example 1(a) Solution contd.
Step Trial 1 Trial 2 Trial n 0. Characteristic strength, Qd 40.0 40.0 0. Post-elastic stiffness, Kd 13.0 13.0 1. Isolator Displacement, Disol 8.08 6.43 2. Effective stiffness, Kisol 17.95 3. Max. isolator force, Fm 144.9 4. Effective period, Teff 1.46 5. Viscous damping ratio, h% 17.6 6. Damping coefficient, BL 1.46 7. Isolator displacement, Disol 6.43
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Example 1(a) Solution contd.
Step Trial 1 Trial 2 Trial n 0. Characteristic strength, Qd 40.0 40.0 40.0 0. Post-elastic stiffness, Kd 13.0 13.0 13.0 1. Isolator Displacement, Disol 8.08 6.43 5.66 2. Effective stiffness, Kisol 17.95 20.06 3. Max. isolator force, Fm 144.9 113.6 4. Effective period, Teff 1.46 1.65 5. Viscous damping ratio, h% 17.6 22.4 6. Damping coefficient, BL 1.46 1.57 7. Isolator displacement, Disol 6.43 5.66
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Example 1(a) Solution contd.
Step Trial 1 Trial 2 Trial n 0. Characteristic strength, Qd 40.0 40.0 40.0 0. Post-elastic stiffness, Kd 13.0 13.0 13.0 1. Isolator Displacement, Disol 8.08 6.43 5.66 2. Effective stiffness, Kisol 17.95 20.06 3. Max. isolator force, Fm 144.9 113.6 4. Effective period, Teff 1.46 1.65 5. Viscous damping ratio, h% 17.6 22.4 6. Damping coefficient, BL 1.46 1.57 7. Isolator displacement, Disol 6.43 5.66
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Examples 1(b) and 1(c)
(b) Adjust Qd in (a) such that the displacement is less
than or equal to 5.0 ins. Neglect pier flexibility. (c) Adjust Qd and Kd in (a) such that the displacement
does not exceed 6.0 ins and the base shear is less than 105 K. Neglect pier flexibility.
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Examples 1(a) - (c) Solutions
Step (a) (b) (c) 0. Characteristic strength, Qd 40.0 49.0 40.0 0. Post-elastic stiffness, Kd 13.0 13.0 10.5 1. Isolator Displacement, Disol 5.66 5.00 5.90 2. Effective stiffness, Kisol 20.06 22.75 17.28 3. Max. isolator force, Fm 113.6 113.8 101.9 4. Effective period, Teff 1.65 1.55 1.77 5. Viscous damping ratio, h% 22.4 27.3 25.0 6. Damping coefficient, BL 1.57 1.66 1.62 7. Isolator displacement, Disol 5.66 5.00 5.90
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Simplified Method
• Basic method assumes near rigid substructures
• Method can be modified to include pier flexibility. See AASHTO Guide Specification Isolation Design, 4th Ed., 2014
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Multimodal Spectral Method
• Elastic Multimodal Method, developed for conventional bridges, may be used for isolated bridges even though they are nonlinear systems.
Modeling the nonlinear properties of the isolators is usually done with equivalent linearized springs and the response spectrum is modified for the additional damping in the ‘isolated modes’.
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Multimodal Spectral Method
• Method is iterative and a good strategy is to use the Simplified Method of Analysis to obtain starting values for the iteration
• Care is required combining the results of individual modal responses which have different damping ratios. Isolated modes have much higher damping than the structural modes, and the CQC method does not easily accommodate this situation. In this case the SRSS method might be preferred.
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Isolator design
• Analysis gives required system properties to meet desired performance (Qd and Kd)
• Next step is to design an isolation system to have these properties
• Isolators used in bridge design include: • Elastomeric bearings with lead cores (Lead-Rubber
Bearing, LRB) • Curved sliders (Concave Friction Bearing, CFB) • Flat plate slider with elastomeric springs (FPS)
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Elastomeric isolator design (LRB)
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Lead-rubber design (LRB)
• Qd = 0.9 d2 (K)
where d = diameter of lead core (in)
• Kd = G Ar / Tr where G = shear modulus of elastomer = 0.1 Ksi, say Ar = bonded area of elastomer Tr = total thickness of elastomer • Shear strain in elastomer, γ = Disol / Tr
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Example 1(a): Lead-rubber design (LRB)
From Example 1(a): • W=533 K and Number of isolators = 12 • Total Qd = 40.0 K (Qd / isolator = 3.33 K) • Total Kd = 13 K/in (Kd / isolator = 1.08 K/in) • Maximum displacement = 5.66 in • Axial load / isolator = 533/12 = 44.42 K Design: Diameter of lead core = √(Qd/0.9) = √(3.33/0.9) = 1.92 ins Assume circular bearing and allowable stress of 800 psi. Then bonded area = 44.42 / 0.8 = 55.52 in2 and bonded diameter = √(4(55.52)/π) = 8.4 in Overall diameter = 8.4 + cover layers = 8.4 + 2 (0.5) = 9.4 in
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Example 1(a) continued (LRB)
Design contd: Thickness of elastomer = GAr / Kd=0.1(55.52)/1.08 = 5.14 in Number of ½ inch layers = 11 Number of 1/8 inch shims = 10 Number of ½ inch cover plates = 2 Overall isolator height = 11 x ½ + 10 x 1/8 + 2 x ½ = 7.75 in Max. shear strain in elastomer = 5.66/5.5 = 103% ok. Solution: Isolation system is set of 12 x 9.4 inch diam. x 7.75 inch high circular bearings, each with a 1.92 inch diam. lead core.
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Concave friction bearings (CFB)
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Concave friction bearing design (CFB)
• Qd = µP where: µ = coefficient of friction P = weight per isolator • Kd = where: R = radius of curvature of slider • Period when sliding =
STAINLESS STEELARTICULATED SLIDER(ROTATIONAL PART)
COMPOSITE LINER MATERIAL
SEAL
R
POLISHED STAINLESS STEEL SURFACE
STAINLESS STEELARTICULATED SLIDER(ROTATIONAL PART)
COMPOSITE LINER MATERIAL
SEAL
R
POLISHED STAINLESS STEEL SURFACE
gRTd π2=
RP
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Example 1(a): Concave friction bearing CFB)
From Example 1(a): • W = 533 K and Number of isolators = 12 • Total Qd = 40.0 K (Qd / isolator = 3.33 K) • Total Kd = 13 K/in (Kd / isolator = 1.08 K/in) • Maximum displacement = 5.66 in • Axial load / isolator (P) = 533/12 = 44.42 K
Design: Friction coefficient µ = Qd / P = 3.33/44.42 = 0.075 Radius of curvature, R = P / Kd =44.42/(1.08) = 41.13 in
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Example 1(a) continued (CFB)
Design continued: • Contact area of slider = P / contact pressure = P / 3000 psi = 44.42/3.0 = 14.80 in2 • Diameter of slider = 4.35 in • Isolator diameter = 2 x max displ. + slider diam. + 2 x shoulders = 2 x 5.66 + 4.35 + 2.0 = 17.67 (18 ins, say) Solution: Isolation system is set of 12 concave friction bearings, 18 in overall diameter, 4.35 in diameter PTFE slider, and 41.13 in radius for stainless steel spherical surface. Probable overall height is about 5 in.
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Question
What are the pros and cons of the two design solutions?
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Summary of LRB and CFB designs
Lead-Rubber Bearing
(LRB)
Concave Friction Bearing
(CFB)
Number of isolators 12 12
External dimensions 9.4 in diam.
x 7.75 in height 18 in diam.
x 5 in (?) height
Internal dimensions 11 x ½ in layers radius = 41 in
Other 1.92 in diam. lead core
coefficient of friction = 0.075
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• Restoring force capability • Clearances (expansion joints, utility crossings… ) • Vertical load capacity and stability at high shear strain • Uplift restrainers, tensile capacity • Non-seismic requirements (wind, braking, thermal
movements… ) • System Property Modification Factors (λ-factors) for aging,
temperature, wear and tear, and contamination • Testing Requirements: characterization tests; prototype
tests; production tests
Other design issues (all isolators)
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Outline
• Conventional vs seismic isolation design • History • Basic requirements (principles) • Examples (applications) • Limitations • Design of a bridge isolation system • Additional sources of information • Design examples • Q&A
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Sources of information
• FHWA/MCEER 2006, Seismic Isolation of Highway Bridges, Special Publication MCEER-06-SP07 • AASHTO 2014, Guide Specifications for Seismic Isolation Design, Fourth Edition
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Sources of information
• Fourth Edition of AASHTO Guide Specification for Seismic Isolation Design published 2014 has design examples in new Appendix B.
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Outline
• Conventional vs seismic isolation design • History • Basic requirements (principles) • Examples (applications) • Limitations • Design of a bridge isolation system • Additional sources of information • Design examples • Q&A
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Design examples
Benchmark Bridge No. 2 Benchmark Bridge No. 1
• 3-span, 25-50-25 ft • 6 PC continuous girders • 3-column piers
• 3-span, 105-152.5-105 ft • 3 steel plate continuous
girders • Single-column piers
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Design examples continued
Benchmark Bridge No. 2 Benchmark Bridge No. 1
7 design examples for each benchmark bridge showing how to design: • For different hazard levels (S1, Site Class) • Various types of isolators (LRB, CFB, FPB) • Bridges with irregular geometry (skew, piers with
different height)
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Design methodology
Step A. Assemble bridge and site data; determine performance objectives
Step B. Analyze bridge in longitudinal direction (i.e. find Qd and Kd to achieve required
performance using (1) simplified method and (2) multi-modal spectral analysis method)
Step C. Repeat in transverse direction
Step D. Combine results from B and C (100/30 rule); check performance
Step E. Design isolation hardware to provide required Qd and Kd
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Design example template
Step number / generic instructions
Step number /
calculations for this
example
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Design example template e.g. Calculation of Effective Period for Benchmark Bridge No. 1
Step number / generic instructions
Step number / calculations for
this example
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Summary of example designs: Set 1
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Summary of example designs: Set 2
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Outline
• Conventional vs seismic isolation design • History • Basic requirements (principles) • Examples (applications) • Limitations • Design of a bridge isolation system • Additional sources of information • Design examples • Q&A
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Questions & Answers